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An Octatonic Essay by Webern: No. 1 of the "Six Bagatelles for String Quartet," Op. 9Author(s): Allen ForteSource: Music Theory Spectrum, Vol. 16, No. 2, (Autumn, 1994), pp. 171-195Published by: University of California Press on behalf of the Society for Music TheoryStable URL: http://www.jstor.org/stable/746032Accessed: 13/05/2008 05:44

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An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

An Octatonic Essay by Webern: No. 1 of the Six Bagatelles for String Quartet, Op. 9

Allen Forte

INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces Example 1. Webern, Op. 7 No. 3: octatonic traces

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

It is not generally known that Webern's atonal music con- tains traces of what has come to be called the octatonic col- lection.1 Indeed, in at least one instance, the first of the com- poser's Bagatelles for String Quartet (1913), the octatonic collection assumes primary importance as organizing force in the pitch domain. This, however, is not its first appearance in Webern's music. Example 1 shows an octatonic "trace" from an earlier work.

The cadential sonority of the penultimate movement of his path-breaking Opus 7, Four Pieces for Violin and Piano (1910), is a hexachord of class 6-Z13, as shown in Example la.2 For devotees of the octatonic who are also familiar with

1"Octatonic collection" refers to the eight-note pitch-class set 8-28. Any one of four orderings will yield what is known as the octatonic scale, defined by the intervallic pattern 1-2-1 ... or 2-1-2 . . . . Whereas, by usage, only the ordered subsets of the scale are of analytical interest, the total array of ordered and unordered subsets of the collection is available for analytical scrutiny. This distinction is basic to the present article, as will become clear. Arthur Berger coined the term octatonic in his article, "Problems of Pitch Organization in Stravinsky," Perspectives of New Music 2 (1963): 11-42.

2I will use set names for pitch-class collections throughout and, where useful, will provide the normal order (not the prime form) of the set in brackets following the name.

a)

-4y

a)

-4y

a)

-4y

a)

-4y

a)

-4y

a)

-4y

a)

-4y

a)

-4y

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1

6-13 [0,1,3,4,6,7 Cl. 6-Z13: [0,1,3,4,6,71 Coll. Il b) 1 2 3 4 5 6 7 8

-9 b, be byF- ^ P 1 s b1 I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

I I I I I I 0 1 3 4 6 7

pitch-class set names, this set identification rings a bell-a strident octatonic bell, in fact-for hexachord 6-Z13 repre- sents one of only two classes of hexachord that can be ex- tracted from the octatonic scale as contiguous (ordered) seg- ments. Example lb demonstrates the location of this form of 6-Z13 in the "ordered" octatonic scale commonly designated

172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum 172 Music Theory Spectrum

Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28 Example 2. Webern, Op. 7 No. 3: the octatonic collection 8-28

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

a) 3 A 3 3-

e 9) 9' e 9) 9' e 9) 9' e 9) 9' e 9) 9' e 9) 9' e 9) 9' e 9) 9'

b) A

b) A

b) A

b) A

b) A

b) A

b) A

b) A

3 3 3 3 3 3 3 3

q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y q,O. 1 ., y

4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1 4-9: [5,6,11,0] I 1

4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il 4 ._ 6k hj bJ i . I il I I I I I I I I I I I I I I I I

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

octatonic scale (or some rotational permutation thereof) will be called "unordered" (with respect to the ordered scale). Accordingly, the two forms of 4-9 in Example 2b exemplify unordered octatonic sets. In contrast, 6-Z13 in Example lb is an ordered form since its members occupy adjacent scalar positions. Because the octatonic scale retains its interval-class sequence (1-2 or 2-1) under simple rotation, an ordered subset may occur in "wrap-around" fashion. For instance, in Example lb 6-Z13 will also be formed by pitch-class mem- bers in locations 7 8 1 2 3 4.

THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE THE SIX BAGATELLES WITHIN WEBERN'S OEUVRE

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

Collection III, after Pieter van den Toorn (see Ex. 7).3 Hexachord 6-Z13 in the third piece of Opus 7 is by no means isolated in that movement. In mm. 6 though 9, as shown in Example 2a, the violin presents the complete octatonic col- lection, comprising two consecutive forms of the same tet- rachordal class, 4-9 [0167]. Example 2b locates these two forms of the tetrachord within the totality of Collection II.

In this configuration (Ex. 2a), octatonic collection 8-28 does not have the familiar form of alternating half and whole steps that we know as the octatonic scale. For the purposes of this article, a subset of the octatonic collection 8-28 in which the members do not occupy adjacent positions in the

3Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 48ff. In Ex. 7 I have taken the liberty of rotating van den Toorn's scales so that his Collection III begins on pitch- class 3 (Eb), Collection II on pitch-class 2 (D) and Collection I on pitch-class 1 (C#).

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

In the summers of 1911 and 1913 Webern composed his Six Bagatelles for String Quartet, Opus 9.4 His prior essay in this medium, the Five Pieces for String Quartet, Opus 5, which dates from 1909, is generally regarded as his first mature atonal composition. Unlike the Opus 5 pieces, however, the Opus 9 miniatures are extremely concise. While the first piece of Opus 5 extends to fifty-five bars, the first piece of Opus 9-the subject of the present study-barely achieves ten. Yet this first piece of Webern's Opus 9 is probably the most com- plex of the set, and not many authors have risen to meet the challenges it offers.5

4Dates are from Hans Moldenhauer and Rosaleen Moldenhauer, Anton von Webern: A Chronicle of His Life and Work (New York: Alfred Knopf, 1979). The first and last pieces were completed in 1913, the others in 1911.

5The longest and most intensive study of Opus 9 in its entirety is: Richard Chrisman, "Anton Webern's 'Six Bagatelles for String Quartet,' Op. 9: The Unfolding of Intervallic Successions," Journal of Music Theory 23 (1979): 81-122. Hasty's trenchant discussion of segmentation issues in Op. 9 No. 1 is especially germane to the octatonic reading in the present article, con- cerning both points of intersection as well as entirely different interpretations of internal musical connections. See Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," Journal of Music Theory 28 (1984): 167-90, esp. 179- 86. Also see footnote 9.

4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91 4-9: [2,3,8,91

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l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'- q v~ - l 'Q 1 `1 b;0L 1 6 "'-

An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173 An Octatonic Essay by Webern 173

Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score Example 3. Webern, Op. 9 No. 1: short score 21 o

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Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

Example 3 presents a short score of the first piece of Opus 9 from which dynamics, articulations, and tempo variations have been excluded in order to give the most concise view of the pitch organization of the work. In addition, the small numerals attached to pitches refer to specific temporal po- sitions in the music-hence, are called p-numbers. The des- ignation P15, for example, refers to g' on the upper stave and to F# on the lower. Because of the presence of these numbers

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

as well as measure numbers on Example 3 it seems advisable to omit triplet identifiers, which are not essential to the an- alytical purpose of the example, in any event.

It is well to bear in mind that-even given the small scale of Webern's compositional output-the Opus 9 Bagatelles are part of a series of ground-breaking works in the key years immediately preceding the First World War. In Webern's oeu- vre this development reached its peak in the Five Pieces for

Moderat A Moderato Moderat A Moderato Moderat A Moderato Moderat A Moderato Moderat A Moderato Moderat A Moderato Moderat A Moderato Moderat A Moderato

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174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum 174 Music Theory Spectrum

Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space Example 4. Total pitch space

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o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

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o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

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~ ~

Wo ho qo ~to "tto e - .' 6 . " *bo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

Wo ho qo ~to "tto e - .' 6 . " *bo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

Wo ho qo ~to "tto e - .' 6 . " *bo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

Wo ho qo ~to "tto e - .' 6 . " *bo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

~ ~

Wo ho qo ~to "tto e - .' 6 . " *bo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

o b2 22 23 24 25 ' 26 27 " 2"8 2o b 3 b3 6 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

Orchestra, Opus 10, completed in 1913. Thus, the Bagatelles should be viewed as part of this development and, in par- ticular, as the successors to the instrumental music of Opus 7, the violin and piano pieces from which the illustrations of Examples 1 and 2 were extracted above.

What is extraordinary about all the Opus 9 compositions is that they are so individualized: each one seems to present its own musical idea, which is composed out in the most meticulous way. It is perhaps this aspect of Webern's atonal music, in addition to its intrinsic aesthetic quality, that con- tinues to attract the attention of scholars interested in in- creasing our understanding of the remarkable avant-garde music of the very early twentieth century. The first piece of Opus 9 is a prime instance.

SURFACE FEATURES OF OP. 9 NO. I

Many of the external aspects of this movement will be familiar to students of Webern's atonal music: the absence of obvious repetition of longer pitch formations and, corre-

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

spondingly, the scrupulous avoidance of traditional themes and motives, the extraordinary attention accorded dynamics, mode of attack, and rhythmic articulation, and the carefully notated expressive changes of tempo-for example, the in- struction heftig at the dynamic climax of the movement in m. 7.

In addition, and of special relevance to the present article, are the registral extremes-notably, the ct4 in violin I at the beginning of m. 8 (p47) and the cello's low C at the end of m. 6 (P36), about both of which more below. Example 4 gives a roster of the entire pitch collection Op. 9 No. 1 unfolds, a total of forty components.

Within this span, gbK and g' occupy the medial position, both spatially, with respect to pitches C and c#4, and nu- merically, with respect to the total number of pitches rep- resented in the music. In the concluding pitch constellation, which encompasses attacks at successive p-numbers P64, P65, P66, and P67, we hear the medial dyad followed by pitch-class representatives of the registral extremes, with c(4 now trans- posed down three octaves to c|tl, while C is transposed up the same distance to become c2. The medial g' descends an

An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175 An Octatonic Essay by Webern 175

Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads Example 5. Alpha and omega dyads

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

octave, leaving only g' (ft 1) in position with respect to the schematic array shown in Example 4. This interlocking arrangement displays the symmetry of the tetrachord, which is of class 4-9 and a member of octatonic collection III (see Ex. 11).

Another significant surface feature consists of the pitches expressed as harmonics. As indicated in Example 4 by the conventional notation for harmonics, only three pitch classes receive this timbral color-those represented by C#, D, and EN -which are also, and significantly so, the first three notes of the piece. In a specific linear sense this minuscule chro- matic cluster is "thematic": each component is the source of

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

a linear octatonic component that is developed throughout the movement.

If this "chromatic cluster" is extended by one note to in- clude cl, the first note played by violin II (which brings all the instruments into the ensemble), it then segments into two dyads, which shall be called alpha and omega, for reasons that will become clear in a moment. Pitch-class specific, contig- uous instances of alpha and omega are displayed in Example 5, together with three motivic derivatives: alpha prime, omega prime, and the compound form, alpha prime/omega prime. Alpha prime and omega prime are derived by in- verting about the constituent monads. Thus, alpha produces

176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum 176 Music Theory Spectrum

(1 2) and (3 4), while omega yields (11 0) and (1 2). But because (1 2) is common to both alpha and omega it is as- signed the label alpha prime/omega prime.

In addition to appearing in occluded form at p55, where it is embedded in the chord, omega occurs together with alpha at P21 through P24 and again at P46 thro